Fortunately, very recent works have addressed theoretical limitations of these methods: One important limitation is the expressive power of NFs.
Because they are based on the change of variables formula, the learned transformations are required to be diffeomorphisms. As a consequence, a NF with bounded Lipschitz constant is unable to map one distribution \(P_{\mathbf {x}}\)  to a lighter-tailed distribution \(P_{\mathbf {z}}\)  [1]}, [2]}.
Therefore, since vanilla NFs are implemented using an isotropic Gaussian base distribution, they are unable to learn heavy-tailed distributions, which are known to appear in natural image data [3]}, [4]}, [5]}.
This is in conflict with observations recently made by [6]}: Even though NFs are typically designed to obey invertibility, this property is often violated in practice.
This is due to numerical inaccuracies, which are promoted by a large Bi-Lipschitz constant. Bounding the Bi-Lipschitz constant, however, conflicts with the previously mentioned theoretical requirements needed to avoid a limited expressiveness of the NF.
